The domain of a function means:
"what x values are possible?"
The range of a function means:
"what y values are possible?"
This difference is just which variable you care about.
For example:
take the equation y=x^2. this is a simple parabola that you hopefully know. the range is anything greater than or equal to 0 because the graph stays above the axis so y is greater than zero. The domain is all real numbers because no matter what x values you choose, a y value exists.
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A relation is a mapping between two sets, a domain and a range. A function is a relationship which allocates, to each element of the domain, exactly one element of the range although several elements of the domain may be mapped to the same element in the range.
Good question. A relation is simply that; any x-value to create any y-value. A function, however, cannot be defined for multiple values of x. In other words, for a relation to be a function, it must have singular values for all x within its domain.
To function means, "to work correctly or adequately". In math, a function is a relation between the domain and the codomain that associates each element in the domain with exactly one element in the codomain.
The domain is all the first coordinates in a relation. A relation is two ordered pairs.
All functions are relations with the condition that each element of the domain is paired with only one element of the range. A relation is any pairing of numbers from the domain to the range.